Computation Ef Electric Field Using FEM Aproach

8/3/2019 Computation Ef Electric Field Using FEM Aproach

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3.2 THEORY

Considering the fact that the electric field analysis is of prime

Importance, the first job is to identify the nature of associated fields. The

influencing factors for the fields are geometry and material property of

medium. Considering a region free of Charges, with the arrangement of

conductors subjected to voltages and dielectrics surrounding the

conductor having permittivity of ∈, the governing field being conservative,

the equation for the field in the region is given by

.(∈ Ф)=0 ( Laplace‟s equation) 3.1

For isotropic homogeneous medium, equation (3.1) further reduces to a

more familiar form called the Laplace‟s equation, viz ;

2Ф=0 3.2

Also equation (3.1) being second order equation, one can specify both

potential and its derivative as the boundary conditions for getting a

unique solution.

3.3 DETAILS OF THE ELECTRODE CONFIGURATION

The most generally encountered electrode configurations for the

study of the physical mechanisms of Coronas are hemispherically capped

cylindrical rod – plane or point plane gaps. In hemispherically capped

cylindrical rod – plane arrangement, by varying the radius of the

electrode tip, different degrees of field nonuniformity can be readily

achieved. The point plane arrangement is particularly suitable for

obtaining a high localized stress. Also such situations are commonly



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encountered in engineering practice. The schematic diagram of the

electrode configuration is shown in Fig. 3.1

Fig. 3.1 Electrode Configuration

„r‟ Radius of tip

„g‟ Gap distance

„L‟ Length of electrode „Rp‟ Radius of grounded plane

electrode

3.4 ESSENTIAL FEATURES OF FEM

The finite element method ( FEM ) is a numerical technique for

finding solutions of partial differential equations as well as of integral

equations encountered in practical engineering problems. The solutions

approach is based either mathematically solving the differential equation

completely ( steady state problems ) using mathematical analytical

methods or rendering the partial differential equation into an

approximating system of ordinary differential equations which are then

numerically integrated using standard techniques such as Euler‟s

method, Runge - Kutta.



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In solving partial differential equations, the primary challenge is to

create an equation that approximates the equation to be studied, but is

numerically stable, meaning that errors in the intermediate calculations

do not accumulate and cause the resulting output to be meaningless.

The Finite element method is a good choice for solving partial differential

equations over complicated domains, when the domain dimensions vary.

The method is elegantly suited for computations of electric field

intensities for different regions of domain by suitably dividing the region

to achieve good accuracy. In view of the above, FEM is employed for

estimation of electric field Intensity which is highly nonuniform in the

entire inter electrode gap of hemispherically capped cylindrical electrode

and plane electrode. In this method, solution is obtained in terms of the

potential itself. Firstly, the whole problem region is fictitiously divided

into small area / volumes called elements. The potential, which is

unknown throughout the region is approximated in each of these

elements in terms of the potential at their vertices called nodes. As a

result of this, the potential function is unknown only at nodes. Normally,

a certain class of polynomials is only used for the interpolation of the

potential inside each element in terms of their nodal values. The

coefficients of this interpolation function are then expressed in terms of

the unknown nodal potentials. As a result of this algebra, the

interpolation can be directly carried out in terms of the nodal values. The

associated algebraic functions are called shape functions. The number of



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vertices and number of terms in the interpolation Polynomial have one to

one correspondence in the iso – parametric element formulation that is

generally employed with FEM for Electrical Engineering Applications.

Elements derive their name through their shape Viz, bar elements in 1 D,

triangular and quadrilateral elements in 2 D and tetrahedron and

hexahedron elements for 3 D problems. Now, for solving the nodal

unknowns, one cannot resort directly to the governing partial differential

equations since a piecewise approximation has been made to the

unknown potential. [1]

Therefore, alternative approaches have to be sought. one of such

classical approach is the calculus of variation. This approach is based on

the fact that potential will distribute in the domain such that the

associated energy will go to minimum ( or lowest extremum ). Based on

this approach, Euler has shown that the potential function that satisfies

the above criteria will be the solution of corresponding governing

equation. In FEM , with the approximated potential function,

extremization of the energy function is sought with respect to each of the

unknown nodal potential. This process leads to a set of linear algebraic

equations. In this matrix form, these equations form normally a

symmetric sparse matrix, which is then solved for the nodal potentials.

3.5 NECESSITY AND DETAILS OF FEM BASED ANSYS SOFTWARE



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The construction of solutions to engineering problems using FEA

requires either the development of a computer program based on the FEA

formulation or the use of a commercially available general purpose FEA

program such as ANSYS. The volume of the equations to be solved is

usually so large that arriving solutions without using computer is

practically impossible. This is the reason for the need of different FEA

packages. one of the many FEA packages available for different

applications is ANSYS. The ANSYS program is a powerful, multipurpose

analysis tool that can be used in a wide variety of Engineering

disciplines. In the present work, ANSYS software version 9.0

[Multiphysics] is used to simulate electric field between point plane

electrodes. The investigator along with guides selected ANSYS Software

Version 9.0 Multiphysics based on discussion with specialists in the field

who are professors in foreign countries . The discussion was also held

with Smt.Ganga Joint director , CPRI Bangalore which supported the

same view .

3.5.1 STEPS TO SOLVE ELECTROSTATIC PROBLEM IN ANSYS

The different steps in a typical ANSYS analysis are :-

Model generation.

Simplifications and Idealizations.

Define materials / material properties.

Generate finite element model.

Specify boundary conditions.



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Obtain the solution.

Review results.

Plot / list results.

Check for validity.

A. BUILD GEOMETRY

If the physical system under consideration exhibits symmetry in

geometry, material properties and loading, then it is computationally

advantageous to model only a representative portion. If the symmetry

observations are to be included in the model generation, the physical

system must exhibit symmetry in all of the following :-

Geometry.

Material properties.

Loading.

Degrees of freedom constraints.

Different types of symmetry are :-

Axisymmetry.

Rotational symmetry.

Plane or reflective symmetry.

Repetitive or Translational symmetry.

In the present work, the model for electrode geometry consisting of

hemispherically capped cylindrical electrode and plane electrode (point

plane gap) has axisymmetry about a central axis. Therefore, the solution

can be obtained representing the electrode geometry as a 2 D model. The



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above symmetry is also valid for the material properties, loading and

constraints. The use of axisymmetric model substantially reduces the

number of nodes and elements resulting in reduction of processing time

required for the solution while delivering the same level of accuracy in

the results.

B. DEFINE MATERIAL PROPERTIES

For the model represented, the appropriate material properties are

given as Inputs to the software program. For electric field calculations,

relative permittivity value of the medium in which the electrodes are

placed is to be given as input.

C. GENERATE MESH

Meshing is a critical operation in FEA . In this operation, the model is

divided Into large number of small pieces. The small pieces are called

mesh or finite elements. In general, a large number of elements provide a

better approximation of the solution, with resulting reduction in analysis

speed. However, in some cases, an excessive number of elements may

increase the rounding off errors. Therefore, it is important that the mesh

is adequately fine or coarse in the appropriate regions to achieve best

results. How fine or coarse the mesh should be in such regions is

another important question. Unfortunately, definitive answers to the

questions about mesh refinement are not available since it is completely

dependent on the specific geometry and domain considered.



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The technique used for mesh generation in the present work is called

“Mesh Refinement Test” within ANSYS. An Analysis with an initial mesh

Is performed first and then reanalyzed by using twice as many elements

as used in the initial analysis. The two solutions are compared. If the

results are close to each other, the initial mesh configuration is

considered to be adequate. If there are substantial differences between

the two, the analysis should continue with a more refined mesh and a

subsequent comparison until convergence is established.

The ANSYS element library contains more than 100 different element

Types. Each element type has a unique number and a prefix that

identifies the element category, Beam4, Plane77, Solid96 etc. The

element type determines among other things, the degree of

freedom(which in turn implies the discipline-structural, thermal,

magnetic, electric, etc) and whether the element lies in two dimensional

or three dimensional space. In the present work, for electrostatic

analysis, Plane121 shown in fig3.2 which is a 2D quadrilateral 8 node

element is used. The element has one degree of freedom which is voltage

at each node. The 8 node elements are well suited to model curved

boundaries and ensure fast convergence even in regions where electric

stress gradient is too steep.



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This element is based on the electric scalar potential formulation and It

is applicable to 2D electrostatic field analysis.

D. LOADING

In terminology of software, this refers to application of 1 volt potential

to point electrode. Field values for other voltages are a suitable

multiplication of these values corresponding to applied voltage.



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E. SOLUTION

The solution of electric field intensity in point plane geometry with

the tip subjected to 1 Volt steady state is a time invariant process. So, a

steady state analysis is performed.

F. PRESENTATION OF RESULTS

After the solution, ANSYS software facilitates to present the results

chosen from many options such as Tables, Graphs and contour plots.

3.5.2 ANSYS PREPROCESSOR

Model generation is conducted in this processor which involves

material definitions, creation of a solid model and finally meshing.

Important tasks within this processor are to specify element type, define

real constants (if required by the element type), define material

properties, Create the model geometry, generate the mesh. Although the

boundary conditions can also be specified in this processor, It is usually

specified in the solution processor.

3.5.3 ANSYS SOLUTION PROCESSOR

This processor is used for obtaining the solution for the finite element

model that is generated within the preprocessor. Important tasks within

this processor are :-

Define analysis type

Specify boundary conditions

Obtain solution



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3.5.4 ANSYS GENERAL POSTPROCESSOR

The Analysis results are reviewed using postprocessors which have

the ability to display contours of potential field results, Vector field

displays, etc.

3.6 DETAILS OF DIMENSIONS OF POINT PLANE GEOMETRY USEDIN

FIELD CALCULATION

Fig. 3.1 shows the sketch of hemi spherically capped cylindrical

plane electrode configuration. Ideally the value of „L‟ should be

enormously high(infinity). However this is not feasible in practice. So in

order to arrive at a suitable practical Value for „L‟ required for

experimental investigations computations were carried out to calculate

the maximum electrical field intensity at the tip for different values of

length of rod Electrode. These calculations were carried out for minimum

value of radius „r‟ of tip ( minimum r=0.4mm).These calculations showed

that for a total length of rod electrode „L‟ greater than two and half times

gap distance „g‟ the calculated maximum field intensity values did not

increase by more than 0.1 % for an increase in length of rod by 4 %.

From these considerations a value of „L‟ equal to two and half times gap

distance (L=2.5g) was selected for computations of electric field

intensities. The value of D used in present investigations is 450mm.

Table 3.1 shows the values of radii of the tip, gap distance and the length

of the cylinder for which calculations were carried for electric field



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intensity. Table 3.2 shows the variation of field intensity with length of

rod electrode.

TABLE 3.1

DIMENSIONS OF POINT PLANE GAP

Radius of tip, r

in mm

Gap distance in

mm

Length of the Rod L in

mm

[1] 0.4 10 25

15 37.5

20 50

30 75

45 112.5

[2] 0.45 20 50

30 75

40 100

45 112.5

50 125

[3] 0.5 10 25

15 37.5

20 50

30 75

45 112.5

[4] 0.6 10 25

15 37.5



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20 50

30 75

45 112.5

[5] 0.75 20 50

30 75

40 100

45 112.5

[6] 1.0 10 25

15 37.5

20 50

30 75

45 112.5

[7] 1.5 10 25

15 37.5

20 50

30 75

45 112.5

[8] 2.5 10 25

15 37.5

20 50

30 75

45 90



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The common procedures followed for computations of electric field

intensities for the above mentioned electrode configurations are :-

Creation of key points Fig 3.3

Creation of lines Fig 3.4

Creation of areas Fig 3.5

Generation of mesh Fig 3.6

Application of loads Fig 3.13 & Fig 3.14

Solution Fig 3.15

TABLE 3.2

VARIATION OF MAXIMUM FIELD INTENSITY WITH LENGTH OF ROD

ELECTRODE

SERIAL

NO

RADIUS

OF TIP, r

IN mm

GAP

DISTANCE

IN mm

LENGTH

OF THE

ROD IN

mm

ELECTRIC

FIELD

INTENSITY

AT THE TIP

V/m

ELECTRIC

FIELD

INTENSITY

AT THE

CATHODE

V/m

[1] 0.4 10 19 1908.92 21.5822

20 1905.66 21.1713

22 1899.82 21.5066

24 1895.5 21.7138

25 1893.25 21.806



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26 1891.66 21.8888

[2] 0.4 15 28.5 1815.29 12.7272

30 1812.17 12.8215

33 1806.67 12.9881

36 1801.81 13.1264

39 1797.74 13.243

3.7 DETAILS OF MAXIMUM FIELD INTENSITIES OBTAINED AT

THE TIP OF POINT ELECTRODE :-

Values of electric field intensities obtained after following the procedure

described in 3.3 is presented in Table 3.3. Also field intensities at the

cathode are presented in Table 3.4. Further the ratio of tangential

component to normal component of electric field intensity at the

electrode air interface is presented in Table 3.5.



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TABLE 3.3

MAXIMUM FIELD INTENSITIES AT THE TIP

SL.NO

Radius of

Tip, r in

mm

Gap distance

in mm

Length of

the rod L in

mm

Maximum

electric field

intensity

At the tip

Volt/metre

[1] 0.4 10 25 1905.66

15 37.5 1812.17

20 50 1716.01

30 75 1653.81

45 112.5 1588.75

[2] 0.45 20 50 1578.38

30 75 1501.49

40 100 1463.65

45 112.5 1448.43

50 125 1420.44

[3] 0.5 10 25 1570.46

15 37.5 1488.66

20 50 1417.96

30 75 1350.9

45 112.5 1296.15



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[4] 0.6 10 25 1342.78

15 37.5 1269.33

20 50 1224.17

30 75 1163.18

45 112.5 1093.89

[5] 0.75 20 50 1006.7

30 75 957.092

40 100 920.274

45 112.5 909.502

[6] 1.0 10 25 872.88

15 37.5 818.122

20 50 773.049

30 75 732.513

45 112.5 692.911

[7] 1.5 10 25 622.217

15 37.5 581.887

20 50 546.3

30 75 515.256

40 100 495.542

48 120 483.956

[8] 2.5 10 25 421.463

15 37.5 384.18



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20 50 363.256

30 75 333.167

45 112.5 313.526

TABLE 3.4

ELECTRIC FIELD INTENSITIES AT THE CATHODE

Sl.no

RADIUS OF

TIP, r in mm

GAP

DISTANCE in

mm

LENGTH OF

THE ROD „L‟

in mm

ELECTRIC

FIELD

INTENSITY

AT THE

CATHODE

V/m

[1] 0.4 10 25 21.1713

15 37.5 12.8215

20 50 8.90961

30 75 5.285

45 112.5 3.25865

[2] 0.45 20 50 9.15076

30 75 5.42087

40 100 3.85218

45 112.5 3.33538

50 125 2.9174



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[3] 0.5 10 25 23.4129

15 37.5 13.755

20 50 9.30142

30 75 5.58253

45 112.5 3.42557

[4] 0.6 10 25 24.9558

15 37.5 14.6296

20 50 9.96852

30 75 5.84523

45 112.5 3.55844

[5] 0.75 20 50 10.6375

30 75 6.20025

40 100 4.38092

45 112.5 3.76251

[6] 1.0 10 25 30.1372

15 37.5 17.2742

20 50 11.6824

30 75 6.75156

45 112.5 4.0666

[7] 1.5 10 25 35.3158

15 25 19.8872

20 50 13.5906



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30 75 7.69077

40 100 5.32821

48 120 4.20075

[8] 2.5 10 25 43.4438

15 37.5 24.611

20 50 16.3513

30 75 9.36479

TABLE 3.5

RATIO OF TANGENTIAL COMPONENT OF ELECTRIC FIELD

INTENSITY TO NORMAL COMPONENT OF ELECTRIC FIELD

INTENSITY AT THE ELECTRODE - AIR INTERFACE

R = 0.4, G = 10mm, L = 20mm

E TANGENTAL ENORMAL E T/EN %

5.87 e-4 1905.5 3.08 e-5

-5.1555 e-3 1905.1 2.706 e-4

4.60655 e-3 1904.5 2.418 e-4

0.0107561 1903.5 5.6506e-4

3.92145e-3 1902.3 2.0614e-4

-4.07179e-3 1900.8 -2.1421e-4

8.994929e-4 1899.1 4.7364e-5

-3.87578e-3 1897.1 2.043e-4

2.88897e-3 1894.8 1.5246e-4



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-0.023434 1892.2 1.2384e-3

-0.0114087 1889.3 6.0385e-4

8.45876e-3 1886.2 4.4845e-4

-0.015455 1882.7 -8.2089e-4

0.0361156 1879 1.922e-3

-0.02429 1874.9 -1.2955e-3

1.908e-3 1870.6 1.0199e-4

-0.019 1865.9 -1.0182e-3

0.01354 1860.9 7.276e-4

0.02272 1855.6 1.2244e-3

0.069719 1849.9 3.7687e-3

0.03223 1843.9 1.7479e-3

-0.01412 1837.6 -7.6839e-4

0.05779 1830.8 3.1565e-3

0.011619 1823.7 6.3711e-4

0.0 1816.2 0.0

-0.02434 1808.3 -1.346e-3

0.04323 1800 2.4016e-3

-0.01145 1791.2 6.3923e-4

0.02266 1782 1.2716e-3

-9.5474e-3 1772.3 -5.387e-4



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0.01648 1762.1 9.3524e-4

9.84753e-3 1751.3 5.6229e-4

3.47996e-3 1740.1 1.9998e-4

0.01616 1728.2 9.3507e-4

0.06554 1715.6 3.8202e-3

0.010457 1702.4 6.1425e-4

0.0172 1688.5 1.0186e-3

0.01385 1673.8 8.2745e-4

0.06589 1658.2 3.9735e-3

0.0511 1641.6 3.1128e-3

0.05488 1624 3.3793e-3

0.05231 1605.3 3.2585e-3

0.040378 1585.2 2.5471e-3

0.04422 1563.5 2.8282e-3

0.04597 1540 2.985e-3

0.05374 1514.3 3.5488e-3

0.04529 1485.9 3.0479e-3

0.08055 1453.6 5.5414e-3

-0.01247 1417.9 -8.7946e-4

-0.12459 1350.3 -9.2268e-3

-0.60341 732.62 -0.0823

2.0803 679.01 0.306



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-0.54521e-1 655.3 8.32e-3

0.21011 633.33 0.03317

0.73261e-1 623.54 0.01174

0.66156e-1 616.44 0.01073

0.37976e-1 612.15 6.203e-3

0.22026e-1 609.68 3.6127e-3

0.66306e-2 608.65 1.0893e-3

-0.62773e-2 608.63 1.0313e-3

-0.18506e-1 609.51 3.0362e-3

-0.30878e-1 611.12 -5.0526e-3

-0.42003e-1 613.39 -6.8476e-3

-0.54862e-1 616.23 -8.9028e-3

-0.67610e-1 619.54 -0.01091

-0.80415e-1 623.37 -0.0129

-0.9607e-1 627.67 -0.0153

-0.11173 632.41 -0.01766

-0.13001 637.6 -0.02039

-0.14939 643.26 -0.02322

-0.17232 649.39 -0.0265

-0.19886 656.01 -0.0303

-0.22784 663.16 -0.0343

-0.25861 670.89 -0.0385



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-0.30998 679.2 -0.0456

-0.32603e-1 688.3 -4.7367e-3

-5.7427 704.47 -0.815

-0.14492 750.47 -0.0193

-0.65034e-1 762.73 -8.526e-3

-0.37333e-1 773.92 -4.8238e-3

-0.19453 788.64 -0.02466

-0.28219 805.04 -0.03505

-0.42214 824.47 -0.0512

-0.54013 847.15 -0.0637

-0.71244 873.93 -0.0815

-0.97595 906.77 -0.1076

-3.8027 950.25 -0.4

-1.8026 1020.9 -0.1765

1.2681 1120.1 0.1132

-1.3563 921.28 -0.1472

-0.85058 923.32 -0.0921

-1.3039 930.99 -0.14005

-0.70236 945.09 -0.0743

-0.64341e-1 972.58 -6.615e-3

0.9059 1011.4 0.0895

0.83692 1068.7 0.0783



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1.754 1151.7 0.15229

9.9973 1266.2 0.78955

39.666 1499.2 2.6458

3.8 MAXIMUM FIELD INTENSITY AS CALCULATED FROM

EXPRESSIONS FOR FIELD NON UNIFORMITY FACTOR

The mean electric field over a distance d between two electrodes with

a Potential difference of V12 is [2]

Eav =

12V

d .3.3

In nonuniform fields, the field nonuniformity factor (f) is defined as

the ratio of maximum value to average value of electric field intensity.

f =m

av

E

E 3.4

Field non uniformity factors have been given in graphical form [ 3,4,5

] or in tables [ 6,7,8 ] by some investigators. An expression has also been

suggested [8] as an approximation of the field nonuniformity factor when

the gap length S is atleast 50 times as large as the rod end radius r.

0.6 , 50S S

f r r

3.5

However, there are many cases when rod plane gaps are used with

rather small s/r ratios.



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Y.Qiu [9] has presented two simple expressions of the field

nonuniformity factor for the hemispherically capped rod plane gap with

s/r ranging from 1 to 500.

6ln

0.45 , 3< 500

ln

S

S Sr f

Sr r

r

3.6

30.85*(1 ), S

r

s f r

3.7

Equations (3.6) and (3.7) can be used for s/r ranging from 1 to 500,

with an accuracy within 5% which is sufficient for engineering

application purpose. Using expressions 3.3, 3.4, 3.6 and 3.7, maximum

field intensity at the tip is computed and presented in Table 3.6.

TABLE 3.6

Maximum Electric Field Intensities as Computed by Using

Expressions for ‘F’ as Given by QIU

Sl.no

Radius

of tip, r

in mm

Gap

distance

S in

mm

S/r Em/EAV

EAV

V/m

Em V/m

[1] 0.4 10 25 17.512 100 1751.2

15 37.5 25.217 66.66 1680.96

20 50 32.8 50 1640

30 75 47.756 33.33 1591.707

45 112.5 69.83 22.22 1551.62



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[2] 0.45 20 44.44 29.44 50 1472

30 66.66 42.794 33.33 1426.32

40 88.88 55.96 25 1399

45 100 62.508 22.22 1388.927

50 111.11 69.0178 20 1380.356

[3] 0.5 10 20 14.38 100 1438

15 30 20.6118 66.66 1373.98

20 40 26.74 50 1337

30 60 38.815 33.33 1293.703

45 90 56.626 22.22 1258.23

[4] 0.6 10 16.66 12.272 100 1227.2

15 25 17.512 66.66 1167.35

20 33.33 22.66 50 1133

30 50 32.8 33.33 1093.22

45 75 47.75 22.22 1061.005

[5] 0.75 20 26.66 18.543 50 927.15

30 40 26.74 33.33 891.2442

40 53.33 34.8117 25 870.2925

45 60 38.815 22.22 862.469

[6] 1.0 10 10 8.0 100 800

15 15 11.216 66.66 747.66

20 20 14.382 50 719.66



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30 30 20.611 33.33 686.96

45 45 29.78 22.22 661.71

[7] 1.5 10 6.66 5.829 100 582.9

15 10 8.0 66.66 533.28

20 13.33 10.148 50 507.4

30 20 14.382 33.33 479.352

40 26.66 18.544 25 463.6

48 32 21.84 20.83 454.927

[8] 2.5 10 4 4.126 100 412.6

15 6 5.4 66.66 359.964

20 8 6.7 50 335

30 12 9.293 33.33 309.735

45 18 13.121 22.22 291.55

Graphs of Electric Field intensity along the axis of a hemispherically

Capped cylinder for different radii r=0.4mm, 0.45mm, 0.5mm, 0.6mm,

0.75mm,1.0mm,1.5mm and 2.5mm and different gap lengths G=10mm

15mm,20mm,30mm,40mm,45mm are shown in Fig. 3.7, 3.8, 3.9, 3.10,

3.11 and 3.12.



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71



72



73



74



75



76



77



78



79



80



81



82

Figure 3.13 Application of loads to FEM Model



83

Figure 3.14 Application of loads to FEM Model (Enlarged view)



84

Figure 3.15 Electric Field Intensity Solutions (Query Results along the

Axis)



85

Figure 3.16 Plot of length of rod L in mm vs Gap distance in mm

Figure 3.17 Plot of Electric field intensity at the tip in V/m vs length of

rod in mm



86

Figure 3.18 Plot of electric field intensity at the cathode in V/m vs Length

of rod in mm.

Figure 3.19 Plot of maximum electric field intensity at the tip in V/m vs

gap distance in mm.



87

Figure 3.20 Plot of electric field intensity at the cathode in V/m vs Gap

distance in mm.

3.9 CONCLUSIONS

The computational investigations using ANSYS (Multiphysics ),

version 9.0 software has resulted in the following conclusions.

1. The ANSYS (Multiphysics ), version 9.0 software can be used to

calculate electric field intensity values between point plane gaps for

entire interelectrode gap spacing for different electrode geometries.

2. For the point plane gaps and for radius of hemispherical tip value

0.5mm and above, the electric field intensity does not vary by more

than 0.1 % over a distance of one mean free path in air at

atmospheric pressure.

3. The maximum value of field intensity on the hemispherical central tip

of point electrode using ANSYS software for point plane gaps is in

good agreement with corresponding values published in literature [ ].



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4. Suitable dimensional details have been designed for point plane gaps

for carrying out experimental investigations and obtain results to good

accuracy [ Refer section 3.6 , page 52 ] .

3.10 REFERENCES

1. Matthew N.O.Sadiku “Elements of Electromagnetics”,2004

ISBN:01-19-513477-X Oxford University Press, New York.

2. M.S.Naidu, V.Kamaraju “High voltage Engineering”, 1997,

ISBN:0-07-4662286-2, Tata McGraw. Hill publishing company

limited New Delhi.

3. H.Steinbigler, “Anfangsfeldstarken und Ausnutzungsfaktoren

rotationssymmetrischer Elektrodenanordnuugen in Luff ”, PhD

thesis Technical university of Munich, 1969

4. H.M.Ryan, “Electric Field of a rod-plane spark gap”, IEE

proceedings, vol.117,pp,283-284,1970

5. R.Brambilla, A.pigini, “Electric field strength in typical high voltage

Insulation”, International symposium on High voltage Engineering,

Zurich, September 1975

6. A.A.Azer, R.P.Comsa, “Influence of field nonuniformity on the

breakdown Characteristics of sulfur hexafluoride”, IEEE

Transactions on Electrical Insulation, vol. EI-8,pp. 136-142,1973.

7. Y.Safar, N.H.Malik, A.H.Qureshi, P.H.Alexander, “Effect of

grounded enclosure On the field distribution of Rod-Plane gaps”,



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Gaseous Dielectrics 111 (Edited by L.G.Christophorou), pergamon

press, pp.522-526,1982.

8. E.S.Kolechitsky, “Calculation of Electric Field of high voltage

installations”, Energoatom press, Moscow,pp.46-49,1983,(in

Russian)

9. Qiu. “Simple Expressions of field non uniformity factor for

hemispherically Capped rod plane gaps”, IEEE Trans on E.I Vol

21, PP 673 – 675, 1986.

CHAPTER – 4

APPARATUS AND EXPERIMENTAL TECHNIQUE

4.1 INTRODUCTION

A description of the apparatus used, the experimental procedure

followed in nonuniform field studies and the measurement technique

used for the measurement of various quantities during the investigations

are presented in this chapter.

4.2 EXPERIMENTAL STUDY

The corona inception potentials mentioned in previous chapters can

be computed from a knowledge of current multiplication in non uniform

field gaps. This requires the measurement of initiatory current and the

current at corona onset. Also, the experimental determination of corona

onset voltage is required for comparison with computed values of the



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same. The numerical investigations do not consider possible influence, if

any, of the polarity of the applied voltage and the type of material.

In the present study, corona inception voltages have been determined

for different materials and radii of hemispherically capped electrodes

from experiments for D.C. Voltage applications of both polarities. Also,

the experimental set up enabled the measurement of rise time of corona

pulses and investigations on negative polarity coronas.

Computation Ef Electric Field Using FEM Aproach

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